Question

understanding the volume of pyramids
the square pyramid shown has a volume of 120 ft.³.
side = 6 ft.
a)
what is the area of the base?
36 ft.²
explanation
✓ thats correct. well done!
b)
find the height of the pyramid.
round your answer to the nearest tenth of a meter.

Explanation:

Step1: Recall pyramid volume formula

The volume $V$ of a pyramid is given by $V = \frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height.

Step2: Identify known values

We know $V = 120\ \text{ft}^3$, and from part (a), $B = 36\ \text{ft}^2$. Substitute into the formula:
$120 = \frac{1}{3} \times 36 \times h$

Step3: Simplify and solve for $h$

First calculate $\frac{1}{3} \times 36 = 12$, so:
$120 = 12h$
$h = \frac{120}{12} = 10$
(Note: The prompt mentions "nearest tenth of a meter" but all given units are feet; assuming this is a typo, the height in feet is 10, which converts to $10 \times 0.3048 = 3.048 \approx 3.0$ meters if unit conversion is required, but the logical answer in the given unit is 10 ft.)

Answer:

10 ft (or 3.0 meters if converting to meters as noted in the prompt)